Answer:
First, express the fraction in <u>partial fractions</u>
Write it out as an identity.
As the denominator has a <u>repeated linear factor</u>, the power of the repeated factor tells us the number of times the factor should appear in the partial fraction. A factor that is squared in the original denominator will appear in the denominator of two of the partial fractions - once squared and once just as it is:
Add the partial fractions:
Cancel the denominators from both sides of the original identity, so the numerators are equal:
Now solve for A and C by <u>substitution</u>.
Substitute values of x which make one of the expressions equal zero (to eliminate all but one of A, B and C):
Find B by comparing coefficients:
Replace the found values of A, B and C in the original identity:
Now integrate: